Order-preserving Pattern Matching Research Articles

Order-Preserving Pattern Matching with Partition

Order-preserving pattern matching, which considers the relative orders of strings, can be applied to time-series data analysis. To perform a more meaningful analysis of time-series data, approximate criteria for the order-isomorphism are necessary, considering diverse types of errors. In this paper, we introduce a novel approximation criterion for the order-isomorphism, called the partitioned order-isomorphism. We then propose an efficient O(n+sort(m))-time algorithm for the order-preserving pattern matching problem considering the criterion of partition. A comparative experiment demonstrates that the proposed algorithm is more effective than the exact order-preserving pattern matching algorithm.

Order-preserving pattern matching with scaling

Given a text T and a pattern P, the order-preserving pattern matching (OPPM for short) problem is to find all substrings of T which have the same relative orders as P. Recently, approximate OPPM that allows errors have been studied such as OPPM with k-mismatches. In this paper we define the OPPM with scaling which is a novel criteria for approximate OPPM by considering the relative orders of cusps and the scale of lengths of strings between them. Also we present an algorithm to solve the OPPM problem with scaling in O(n+mlog⁡m) time, which is the same time bound as the best known exact OPPM algorithm.

Order-preserving pattern matching indeterminate strings

Given a pattern p of size m and a text t, the problem of order-preserving pattern matching (OPPM) is to find all substrings of t that satisfy one of the orderings defined by p. This problem has applications on time series analysis. However given its strict nature this model is unable to deal with indetermination, thus limiting its application to noisy time series. In this paper we introduce indeterminate characters to alleviate this limitation. We then propose two polynomial time algorithms. If the indetermination is limited to p confirming one occurrence can be computed in O(rmlg⁡r) time, where r is a bound on the number of uncertain characters per position. If the indetermination alternates, but does not occur at the same position in t and p, we present an algorithm that requires O(rm(m+log⁡r)) time. We also show that the general problem is NP-hard and provide a polynomial size boolean formula.

The order-preserving pattern matching problem in practice

Given a pattern x of length m and a text y of length n, both over a totally ordered alphabet, the order-preserving pattern matching (OPPM) problem consists in finding all substrings of the text with the same relative order as the pattern. The OPPM problem, which might be viewed as an approximate variant of the well-known exact pattern matching problem, has gained attention in recent years. This interesting problem finds applications in such diverse fields as time series analysis (as share prices on stock markets or weather data analysis) and musical melody matching, just to mention a few.In this paper we present two new filtering approaches which turn out to be much more effective in practice than the previously presented methods, reducing the number of false positives up to 99%. We also present a new efficient approach inspired by the well-known Skip Search algorithm for the exact string matching problem. It makes use of efficient SIMD SSE instructions for speeding up the searching phase. Experimental results show that our proposed algorithms are up to twice faster than previous solutions.

Z-함수를 이용한 순위패턴매칭과 순위다중패턴매칭 병렬계산

Disclosed is a z-function-based parallel computation method for order-preserving pattern matching and order-preserving multiple pattern matching. Provided is a z-function-based parallel computation method, which includes a step of calculating a z-function which is a maximum length at which a prefix of a suffix CC starting at each position BB with respect to a character string AA of length n coincides with a prefix of a character string S. According to an embodiment of the present invention, it is possible to provide a parallel algorithm using a z-function, which can solve order-preserving pattern matching using DD threads for an EE time.

On Representations of Ternary Order Relations in Numeric Strings

Order-preserving matching is a string matching problem of two numeric strings where the relative orders of consecutive substrings are matched instead of the characters themselves. The order relation between two characters is a ternary relation (>, <, $$=$$ ) rather than a binary relation (>, <), but it was not sufficiently studied in previous works [Cho et al. (Fast order-preserving pattern matching, 2013), Kim et al. (Theor Comput Sci 525:68—79, 2014), Kubica et al. (Inform Process Lett 113:430–433, 2013)]. In this paper, we extend the representations of order relations by Kim et al. (Theor Comput Sci 525:68—79, 2014) to ternary order relations, and prove the equivalence of those representations. With our extensions, the time complexities of order-preserving matching in binary order relations can be achieved in ternary order relations as well.

순위다중패턴매칭을 위한 해싱기반 알고리즘

순위패턴매칭문제는 텍스트 T와 패턴 P가 주어질 때, P와 각 문자들의 순위가 동일한 순서로 나타나는 T의 모든 부분문자열을 찾는 문제이다. 순위패턴매칭문제는 주가지수분석과 음악의 유사성분석과 같이 문자 자체를 비교하는 것보다 값의 변화순서가 중요한 분야에서 연구가 진행되었다. 순위다중패턴매칭문제는 텍스트 T와 여러 개의 패턴들로 이루어진 패턴집합 ℙ가 주어질 때, ℙ에 속한 패턴과 각 문자들의 순위가 동일한 순서로 나타나는 T의 모든 부분문자열을 찾는 문제이다. 본 논문에서는 순위다중 패턴매칭문제를 해결하는 해싱기반 알고리즘을 제시한다.

Generalized pattern matching and periodicity under substring consistent equivalence relations

Let ≈ be a substring consistent equivalence relation (SCER) on strings such that for any two strings x,y, x≈y implies that (1) |x|=|y| and (2) x[i..j]≈y[i..j] for all 0≤i≤j<|x|. Examples of SCER are parameterized pattern matching and order-preserving pattern matching. We present a generalized and efficient algorithm for pattern matching with SCER ≈. Also, we show analogues of Fine and Wilf's periodicity lemma hold for SCER.

Order-preserving pattern matching with k mismatches

We consider a generalization of the recently introduced order-preserving pattern matching. The difference between the standard pattern matching and the order-preserving variant is that instead of looking for an exact copy of the pattern, we only require that the relative order between the elements is the same. In our generalization, we additionally allow up to k mismatches between the pattern of length m and the text of length n, and the goal is to construct an efficient algorithm for small values of k. Our solution detects an order-preserving occurrence with up to k mismatches in O(n(log⁡log⁡m+klog⁡log⁡k)) time.

Order-preserving indexing

Kubica et al. [33] and Kim et al. [29] introduced order-preserving pattern matching: for a given text the goal is to find its factors having the same ‘shape’ as a given pattern. Known results include a linear-time algorithm for this problem (in case of polynomially-bounded alphabet) and a generalization to multiple patterns. We propose an index that enables order-preserving pattern matching queries in time proportional to pattern length. The index can be constructed in O(nlog⁡log⁡n) expected time or in O(nlog2⁡log⁡n/log⁡log⁡log⁡n) worst-case time. It is an incomplete order-preserving suffix tree which may miss a single edge label at each branching node. For most applications such incomplete suffix trees provide the same functional power as the complete ones. We show a number of their applications, including computation of longest common factors, longest previously occurring factors and squares in a string in the order-preserving setting. We also give an O(nlog⁡n)-time algorithm constructing complete order-preserving suffix trees.

Order preserving pattern matching revisited

In this paper, we study the order preserving pattern matching (OPPM) problem, which is a very recent variant of the classic pattern matching problem. We revisit this variant, present a new interesting pattern matching algorithm and for the first time consider string regularities from this new perspective.

A fast algorithm for order-preserving pattern matching

Given a text T and a pattern P, the order-preserving pattern matching (OPPM) problem is to find all substrings in T which have the same relative orders as P. The OPPM has been studied in the fields of finding some patterns affected by relative orders, not by their absolute values. In this paper, we present a method of deciding the order-isomorphism between two strings even when there are same characters. Then, we show that the bad character rule of the Horspool algorithm for generic pattern matching problems can be applied to the OPPM problem and we present a space-efficient algorithm for computing shift tables for text search. Finally, we combine our bad character rule with the KMP-based algorithm to improve the worst-case running time. We give experimental results to show that our algorithm is about 2 to 6 times faster than the KMP-based algorithm in reasonable cases.